Question

In the diagram below, DE is parallel to AB in right triangle ABC. DE bisects AC and CB. If AD = 3, and CB = 5, what is the length of DE?
А
D

Answer 1

The length DE is the hypotenuse of triangle CDE

The length DE is $\frac{\sqrt{61}}2$

How to determine the length DE

The given parameters are:

$AD =3$

$CB = 5$

Given that line DE bisects AC and CB, it means that:

$CD = AD = 3$

$CE = EB = 2.5$ i.e. CB/2

So, we have:

$DE =\sqrt{AD^2 + CE^2$ --- Pythagoras theorem

Substitute known values

$DE =\sqrt{3^2 + 2.5^2$

$DE =\sqrt{15.25$

Express as fraction

$DE =\sqrt{\frac{61}{4}$

Simplify

$DE =\frac{\sqrt{61}}2$

Hence, the length DE is $\frac{\sqrt{61}}2$

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